Probability - MCQ 5 - Bank Exams MCQ

(P = pass, F = fail)
A_passB_fail + A_failB_pass
PF + FP
1/3*2/5 + 2/3*3/5 = 8/15

we can solve this by calculating the probability of the opposite event (no boys selected) and subtracting it from 1 (since probabilities of all events must sum to 1).

Here's how:

Step 1: Probability of no boys selected (unfavorable event)

• We can choose 4 girls out of 6 girls in ⁶C₄ ways (combinations, order doesn't matter).
• The total number of ways to choose 4 members from 11 (5 boys + 6 girls) is ¹¹C₄ ways.

Probability (no boys) = Favorable cases (girls only) / Total cases = ⁶C₄ / ¹¹C₄

Step 2: Probability of at least one boy (favorable event)

Probability (at least one boy) = 1 - Probability (no boys)

Calculation:

⁶C₄ = (6 * 5 * 4 * 3) / (4 * 3 * 2 * 1) = 15 ¹¹C₄ = (11 * 10 * 9 * 8) / (4 * 3 * 2 * 1) = 330

Probability (no boys) = 15 / 330 = 1/22

Probability (at least one boy) = 1 - (1/22) = 21/22

Therefore, the probability that at least one boy is selected is 21/22.

1 – 1/2*2/3*5/6 = 13/18

Total Number of balls = 4 +5 +6 =15 balls
neither red nor white 
means it is Green
so P = no of green ball / Total Number of Balls
P = 5/15 = 1/3

Total number of outcomes = 7*7*7*7
Favourable outcome = 7*6*5*4
P = (7*6*5*4)/7*7*7*7 = 120/343

Total number of outcome = 6*5*4*3*2
Favourable outcome = 5*4*3*2. So, P = 1/6

4/52*4/51

prob. That man is not alive = 3/4 and that of his wife = 3/5
Prob. That both will be dead = 3/4*3/5 = 9/20

= Total outcomes = {HHH,HTH,HHT,THH,TTT,TTH,THT,HTT}
Favourable outcome = HHH, HTH, HHT,THH
Prob = 4/8 = 1/2

Favourable outcome = TTH, THT, HTT
So, prob. = 3/8

17C3 = 17*16*15/3*2*1 = 4080/6 = 680
3C3 = 1
P = 1/680

17C5 = 17*16*15*14*13/5*4*3*2*1 = 742560/120 = 6188
11C5 = 11*10*9*8*7/5*4*3*2*1 = 55440/120 = 462
P = 462/6188 = 33/442

17C3 = 17*16*15/3*2*1 = 4080/6 = 680
4C1 × 4C2 = 4*4*3/2*1 = 24
P = 24/680 = 3/85

14C4 = 14*13*12*11/4*3*2*1 = 1001
4 No positive+4 no negative + (2 no positive * 2 no negative)
= 6C4 + 8C4 +(6C2 ×8C2) = 15+70+15*28 = 505
P = 505/1001

5! = 5*4*3*2*1 = 120
4! = 4*3*2*1 = 24
P = 24/120 = 1/5

13C2 = 13*12/2 =78
2C2 = 1
P = 1/78

1/2 * 1/6 = 1/12

=4C1×4C1×4C1 / 52C3
=4×4×4 / 22100
=16/5525

n(S) = 36
n(E) = (2,3),(2,6),(4,3),(4,6),(6,3),(6,6),(3,2),(6,2),(3,4),(6,4),(3,6)
P = 11/36

E = (1, 1), (1, 2), (1, 4), (1, 6), (2, 1), (2, 3), (2, 5), (3, 2), (3, 4), (4, 1), (4, 3), (5, 2), (5, 6), (6, 1), (6, 5)
n(E) = 15
n(S) = 6*6 = 36
P = 15/36 = 5/12