Question

1. . The probability of connecting to an electronic communication system is 0.8. Suppose that attempts are made to connect until 2 successful connections have occurred.
1) What is the probability that 6 attempts are needed?
2) What is the probability that less than 6 attempts are needed?

2. Three people throw a coin and the uneven one pays refreshments. If all the coins have the same results, they throw themselves again. Find the probability that it need less than 4 releases.
Answer:

**please answer both. THANKS!

Answer 1

Binomial distribution: P(X) = nCx p^x q^n-x

1. P(connecting), p =0.8

q = 1 - p = 0.2

1) P(6 attempts are needed) = P(1 successful connection in first 5) x P(6th attempt is successful)

= (5C1 x 0.8 x 0.2⁴) x (0.8)

= 0.00512

2) P(less than 6 attempts are needed) = 1 - P(at least 6 attempt is needed)

= 1- [P(0 successful connection in first 5 attempts) + P(1 successful connection in first 5)]

= 1 - [0.2⁵ + 5C1 x 0.8 x 0.2⁴]

= 1 - 0.00672

= 0.99328

2. P(less than 4 releases) = 1 - P(4 or more releases)

= 1 - [P(all heads on first 3 releases) + P(all tails on first 3 releases)]

= 1 - (0.5³ + 0.5³)

= 0.75