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3 problems match “binomial distribution”. Clear

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1. Two heads and two tails ●○○○○ 10 ptsFour fair coins are tossed simultaneously. What is the probability that exactly two coins show heads and two show tails? Give your answer as a decimal.
2. Exactly two sixes in three rolls ●○○○○ 10 ptsLet $X$ be the number of sixes obtained in three rolls of a fair six-sided die, so $X \sim \text{Bin}(3, \tfrac{1}{6})$. Find $P(X = 2)$. Round to three decimal places.
3. Equal heads from two coins ●●○○○ 20 ptsCoin $A$ is flipped three times and coin $B$ is flipped four times. Both coins are fair. What is the probability that the number of heads obtained from coin $A$ equals the number of heads obtained from coin $B$? Give your answer as a decimal.