Each minute, a faucet allows 4/9 gallons of water to enter a large tub, and the drain allows 8/9 gallons to leave the tub.
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Answer:
Probability both are nervous around strangers = 0.0049
Probability at least one is nervous around strangers = 0.1302
Step-by-step explanation:
Let probability a person selected in the population is nervous around strangers = P
P = 7%
P =
P = 0.07
Let probability a person selected in the population is not nervous around strangers = P'
P' = 1 - P
P' = 1 - 0.07
P' = 0.93
(i) probability of the first person selected is nervous around strangers = P
probability of the second person selected is nervous around strangers = P
Probability both are nervous around strangers = (P × P)
= 0.07 × 0.07
= 0.0049
(ii) Probability at least one is nervous around strangers = ( probability the first person is nervous around strangers AND the second person is not nervous around strangers ) OR ( probability the second person is nervous around strangers AND the first person is not nervous around strangers)
This implies,
Probability at least one is nervous around strangers = (P × P') or (P × P')
= (0.07 × 0.93) + (0.07 × 0.93)
= 0.0651 + 0.0651
= 0.1302