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Probability

Short Answer Type

761.

A coin is tossed three times, where
E : at least two heads , F : at most two heads

132 Views

762.

A coin is tossed three times, where
E : at most two tails , F : at least one tail

85 Views

763. A black and a red dice are rolled.Find the conditional probability of obtaining a sum greater than 9, given that the black die resulted in a 5.

104 Views

764. A black and a red dice are rolled. Find the conditional probability of obtaining the sum 8, given that the red die resulted in a number less than 4.

169 Views

Long Answer Type

765. Given that the two numbers appearing on throwing two dice are different. Find the probability of the event ‘the sum of numbers on the dice is 4’.

142 Views

766. An instructor has a question bank consisting of 300 easy True/False questions, 200 difficult True/False questions, 500 easy multiple choice questions and 400 difficult multiple choice questions. If a question is selected at random from the question bank, what is the probability that it will be an easy question given that it is a multiple choice question?

The given data is

	Easy	Difficult	Total
True/False	300	200	500
Multiple Choice	500	400	900
Total	800	600	1400

Let E : Easy questions, D : Difficult questions
T : True/false questions and M : Multiple choice questions
Number of easy multiple choice questions = 500
Total number of questions = 1400
$straight P left parenthesis straight E intersection straight M right parenthesis$ = Probability of selecting an easy and multiple choice question
$equals space 500 over 1400$
Total number of multiple choice questions
= 500 + 400 = 900
P(M) = Probability of selecting one multiple choice question
$equals space 900 over 1400$
$straight P left parenthesis straight E space left enclose straight M right parenthesis space equals space fraction numerator straight P left parenthesis straight E intersection straight M right parenthesis over denominator straight P left parenthesis straight M right parenthesis end fraction space equals fraction numerator begin display style 500 over 1400 end style over denominator begin display style 900 over 1400 end style end fraction space equals 5 over 9$

173 Views

Short Answer Type

767. Find the probability of drawing a king, when a card is drawn from a well shuffled pack of cards. It is also given that the card drawn is a face card.

222 Views

768.

Two coins are tossed once, where
E : tail appears on one coin, F : one coin shows head
Determine P(E | F).

82 Views

769.

Two coins are tossed once, where
E : no tail appears, F : no head appears
Determine P(E | F).

80 Views

770. 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 the youngest is a girl?

104 Views