# A box contains 10 bells. There are 6 red bells and the rest are silver. What is the probability of p

Discussion in 'Calculator Requests' started by math_celebrity, Nov 20, 2018.

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A box contains 10 bells. There are 6 red bells and the rest are silver. What is the probability of picking two bells of the same color if the bell is replaced after each pick?

If there are 6 red bells, then we have 10 - 6 = 4 silver bells.

The problem asks for the probability of picking two bells of the same color. Which mean we have 2 scenarios:
1. Silver, Silver
2. Red, Red
Find the probability of Silver, Silver:
Since each draw is independent, and we replace the bells, we have a 4/10 chance of picking silver. Simplified, this is 2/5.
(2/5)(2/5) = 4/25

Find the probability of Red, Red:
Since each draw is independent, and we replace the bells, we have a 6/10 chance of picking silver. Simplified, this is 3/5.

(3/5)(3/5) = 9/25

Because we want Silver, Silver or Red, Red, we add the two probabilities.
4/25 + 9/25 = 13/25