Q78 / 160 · TS EAMCET 2021 (04 Aug Shift 1) · Mathematics

A, B, C are aiming to shoot a balloon. A will succeed 4 times out of 6 attempts. The chance of B to shoot the balloon is 3 out of 5 and that of C is 2 out of 3. If the three aim to shoot the balloon simultaneously, then the probability that at least two of them hit the balloon is

  • A
    59
  • B
    925
  • C
    3245
  • Correct answer
    D
    49

Solution

Probability of winning of A =P(A)=46=23

⇒P(A¯)=1-P(A)=13

Probability of winning of B =P(B)=35

⇒P(B¯)=1-P(B)=25

Probability of winning of C =P(C)=23

⇒P(C¯)=1-P(C)=13

Probability of winning atleast means one player will loose =P(A¯)P(B)P(C)+P(A)P(B¯)P(C)+P(A)P(B)P(C¯)

=13×35×23+23×25×23+23×35×13

=49

Hence, the correct answer is option: 'D'.

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