Mathematics : Probability

Two decks of playing cards are well shuffled and 26 cards are randomly distributed to a player. Then, the probability that the player gets all distinct cards is

• ${}^{52}\mathrm{C}_{\mathrm{r}}/{}^{104}\mathrm{C}_{26}$

• $2 \times {}^{52}\mathrm{C}_{\mathrm{r}}/{}^{104}\mathrm{C}_{26}$

• $2^{13} \times {}^{52}\mathrm{C}_{\mathrm{r}}/{}^{104}\mathrm{C}_{26}$

• $2^{26} \times {}^{52}\mathrm{C}_{\mathrm{r}}/{}^{104}\mathrm{C}_{26}$

An um contains 8 red and 5 white balls. Three balls are drawn at random. Then, the probability that balls of both colours are drawn is

• $\frac{40}{143}$

• $\frac{70}{143}$

• $\frac{3}{13}$

• $\frac{10}{13}$

Let A and B be two events with $\mathrm{P}\left({\mathrm{A}}^{\mathrm{C}}\right) = 0.3, \mathrm{P}\left(\mathrm{B}\right) = 0.4 \mathrm{and} \mathrm{P}\left(\mathrm{A} \cap {\mathrm{B}}^{\mathrm{C}}\right)$. Then, $\mathrm{P}\left(\mathrm{B} | \mathrm{A} \cup {\mathrm{B}}^{\mathrm{C}}\right)$ is equal to

• $\frac{1}{4}$

• $\frac{1}{3}$

• $\frac{1}{2}$

• $\frac{2}{3}$

4 boys and 2 girls occupy seats in a row at random. Then the probability that the two girls occupy seats side by side is

• $\frac{1}{2}$

• $\frac{1}{4}$

• $\frac{1}{3}$

• $\frac{1}{6}$

A coin is tossed again and again. If tail appears on first three tosses, then the chance that head appears on fourth toss is

• $\frac{1}{16}$

• $\frac{1}{2}$

• $\frac{1}{8}$

• $\frac{1}{4}$

Two dice are tossed once. The probability of getting an even number at the first die or a total of 8 is

• $\frac{1}{36}$

• $\frac{3}{36}$

• $\frac{11}{36}$

• $\frac{20}{36}$

The probability that at least one of A and B occurs is 0.6. If A and B occur simultaneously with probability 0.3, then P(A') + P(B') is

• 0.9

• 0.15

• 1.1

• 1.2

A and B are two independent events such that P(A $\cup$ B') = 0.8, and P(A) = 0.3. Then, P(B) is

• $\frac{2}{7}$

• $\frac{2}{3}$

• $\frac{3}{8}$

• $\frac{1}{8}$

Three numbers are chosen at random from 1 to 20. The probability that they are consecutive is

• $\frac{1}{190}$

• $\frac{1}{120}$

• $\frac{3}{190}$

• $\frac{5}{190}$

Let E' denote the complement of an event E. Let E, F, G be pairwise independent events such that P(G) > 0 and P(E ∩ F ∩ G) = 0. Then, P(E' $\cap$ F' /G) equals

• P(E') + P(F')

• P(E') - P(F')

• P(E') - P(F)

• P(E) - P(F')