Question

The probability of success is 0.6 for each trial. Find the probability of each:

13 successes in 24 trials

9 successes in 20 trials

6 failures in 12 trials

Please help! Honestly clueless. Only have a few days of school left.

Answer 1

1. 0.1367

2. 0.0709

3. 0.1766

Explanation:

The probability of success is p=0.6, then the probability of a failure is q=1-0.6=0.4.

1. The probability that there are exactly 13 successes in 24 trials is

`C^(24)_(13)p^(13)q^(24-13)=(24!)/(13!(24-13)!)\cdot (0.6)^(13)\cdot (0.4)^(11)\approx 0.1367`

2. The probability that there are exactly 9 successes in 20 trials is

`C^(20)_(9)p^(9)q^(20-9)=(20!)/(9!(20-9)!)\cdot (0.6)^(9)\cdot (0.4)^(11)\approx 0.0709`

3. The probability that there are exactly 6 failures in 12 trials is

`C^(12)_(6)q^(6)p^(12-6)=(12!)/(6!(12-6)!)\cdot (0.4)^(6)\cdot (0.6)^(6)\approx 0.1766`