Probability Model Questions Set 1 Section-Wise Topic Notes With Detailed Explanation And Example Questions

Answer: (e)

Total possible result n(S) = $^{12}C_{2}$ = ${12 × 11}/{1 × 2}$ = 66

Total number of event = n(E) $^4 C _2$ = ${4 × 3}/{1 × 2}$ = 6

∴ Required probability = ${n(E)}/{n(S)}$ = $6/{66}$ = $1/{11}$

Answer: (a)

S = {1, 2, 3, 4, 5, 6}; n(S) = 6

E(not divisible by 3) = 1, 2, 4, 5}, n(E) = 4

∴ P(not divisible by 3) = $4/6$ = $2/3$

Answer: (a)

Total possible result = n(S) = $^{12} C_3$.

= ${12 × 11 × 10}/{1 × 2 × 3}$ = 220 Total number of event = n(E)

Except blue marbles, selection of 3 marbles out of 7 marbles

= $^{7}C_3$ = ${7 × 6 × 5}/{1 × 2 × 3}$ = 35

∴ Required probability = $(1 -{35}/{220}) = (1 - {7}/{44})$ = ${37}/{44}$

Answer: (e)

Probability to be a Blue = ${^3C_3}/{^7C_3}$

Probability to be a Red = ${^4 C_3}/{^7C_3}$

Required probability = ${^3 C_3}/{^7 C_3}$ + ${^4 C_3}/{^7C_3}$ = $2/{35}$

Answer: (d)

Total number of cards = 104 = 2 × 52

and total number of jacks = 8 = 2 × 4

∴ Probability for the jack in first draw = $8/{104}$

and probability for the jack in second draw = $7/{103}$

Since both the events are independent events.

Hence the probability that both of them are jacks.

= ${8}/{104}$ × ${7}/{103}$ = $7/{1339}$