Multiple choice

Box A contains $3$ red and $2$ blue marbles while box $B$ contains $2$ red and $8$ blue marbles. A fair coin is tossed. If the coin turns up heads, a marbles is drawn from $A$, if it turns up tails, a marble is drawn from bag $B$. the probability that a red marble is chosen,is

  1. $\dfrac{1}{5}$
  2. $\dfrac{2}{5}$
  3. $\dfrac{3}{5}$
  4. $\dfrac{1}{2}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The probability of choosing red from box A is 3/5, and from box B it is 2/10 = 1/5. Since each box is selected with probability 1/2, the total probability is (1/2)(3/5) + (1/2)(1/5) = 2/5.

AI explanation

The probability of getting heads on the coin is 1/2, and the probability of getting tails is also 1/2. Box A contains 3 red and 2 blue marbles, so the probability of drawing a red marble from A is 3/5. Box B contains 2 red and 8 blue marbles, so the probability of drawing a red marble from B is 2/10. Using the law of total probability, the required probability is the probability of heads times the probability of red from A plus the probability of tails times the probability of red from B, which is 1/2 times 3/5 plus 1/2 times 2/10. This evaluates to 3/10 plus 1/10, giving 4/10, which simplifies to 2/5. The result is 2/5.

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