A family has two children. What is the probability that both the

Previous Year Papers

Download Solved Question Papers Free for Offline Practice and view Solutions Online.

Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Test Yourself

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.
Advertisement

 Multiple Choice QuestionsShort Answer Type

771. Assume that each born child is equally likely to be a boy or a girl. If a family has two children, what is the conditional probability that both are girls given that at least one is a girl?
84 Views

Advertisement

772.

A family has two children. What is the probability that both the children are boys given that at least one of them is a boy?


Let b stand for boy and g for girl.
∴ S = {(b, b), (g, b), (b, g), (g, g)}
Let E and F denote the following events:
E : ‘both the children are boys’
F : ‘at least one of the child is a boy’
∴  E = {(b, b)} and F = {(b, b), (g, b), (b, g)}
Now,            straight E space intersection space straight F space equals space left curly bracket left parenthesis straight b comma space straight b right parenthesis right curly bracket
 therefore space space space space space space space space straight P left parenthesis straight F right parenthesis space equals space 3 over 4 space and space straight P left parenthesis straight E intersection straight F right parenthesis space equals space 1 fourth
therefore space space space space space space straight P left parenthesis straight E space left enclose straight F right parenthesis space equals space fraction numerator straight P left parenthesis straight E intersection straight F right parenthesis over denominator straight P left parenthesis straight F right parenthesis end fraction space equals space fraction numerator begin display style 1 fourth end style over denominator begin display style 3 over 4 end style end fraction space equals space 1 third

99 Views

Advertisement
773. Mother, father and son line up at random for a family picture
E : son on one end,    F : father in middle,  Determine P(E | F).
111 Views

774.

A couple has two children,
Find the probability that both children are males, if it is known that at least one of the children is male. 

88 Views

Advertisement
775.

A couple has two children,
Find the probability that both children are females, if it is known that the elder child is a female.

98 Views

 Multiple Choice QuestionsLong Answer Type

776.

An electronic assembly consists of two subsystems, say A and B. From the previous testing procedures, the following probabilities are assumed to be known:
P( A fails) = 0.2
P(B fails alone) = 0.15
P(A and B fail) = 0.15
Evaluate the following probabilities:
(i) P( A fails left enclose straight B space has space failed end enclose) (ii) P(A fails alone)

129 Views

777. Consider the experiment of throwing a die, if a multiple of 3 comes up, throw the die again and if any other number comes, toss a coin. Find the conditional probability of the event ‘the coin shows a tail’, given that ‘at least one die shows a 3’.
92 Views

778. Consider the experiment of tossing a coin. If the coin shows head, toss it again but if it shows tail, then throw a die. Find the conditional probability of the event that ‘the die shows a number greater than 4’ given that ‘there is at least one tail.’

130 Views

Advertisement

 Multiple Choice QuestionsMultiple Choice Questions

779.

If straight P left parenthesis straight A right parenthesis space equals space 1 half comma space space space straight P left parenthesis straight B right parenthesis space equals space 0 comma space space then space straight P left parenthesis straight A space left enclose straight B right parenthesis is

  • 0

  • 1 half
  • not defined

  • not defined

77 Views

780. If A and B are events such that P(A|B) = P(B|A), then
  • A ⊂ B but A ≠ B
  • A = B
  • A ∩ B = ϕ
  • A ∩ B = ϕ
79 Views

Advertisement