Question

A player can take a maximum of 4 chances to hit a bottle with a flying disc.The probability of hitting the bottle at the first, second,third and fourth shots are 0.1, 0.2, 0.35 and 0.45 respectively.What is the probability that the player hits the bottle with the flying disc?

• A. 0.6573
• B. 0.2574
• C. 0.7426
• D. 0.3427

Answer 1

The Correct Option is C

The probability of missing the bottle on each shot is calculated as follows:

• Shot 1: \( 1 - 0.1 = 0.9 \)
• Shot 2: \( 1 - 0.2 = 0.8 \)
• Shot 3: \( 1 - 0.35 = 0.65 \)
• Shot 4: \( 1 - 0.45 = 0.55 \)

The probability of missing all 4 shots is:

\[ 0.9 \times 0.8 \times 0.65 \times 0.55 = 0.2874 \]

Therefore, the probability of hitting the bottle at least once in four shots is:

\[ 1 - 0.2874 = 0.7426 \]