This tree diagram shows the tossing of an unfair coin followed by drawing one bead from a cup containing 7 red (R), 4 yellow (Y) and 5 blue (B) beads. For the coin, P(H) = 13 and P(T) = 23 where H is heads and T is tails.Find P(tossing a Head on the coin AND a Red bead). (Enter your answer as a fraction.)
Question
This tree diagram shows the tossing of an unfair coin followed by drawing one bead from a cup containing 7 red (R), 4 yellow (Y) and 5 blue (B) beads. For the coin, P(H) = 13 and P(T) = 23 where H is heads and T is tails.Find P(tossing a Head on the coin AND a Red bead). (Enter your answer as a fraction.)
Solution
To find the probability of two independent events both occurring, you multiply the probabilities of each event.
The probability of tossing a head on the coin is given as 1/3.
The probability of drawing a red bead is the number of red beads divided by the total number of beads. There are 7 red beads and a total of 7 (red) + 4 (yellow) + 5 (blue) = 16 beads. So, the probability of drawing a red bead is 7/16.
Therefore, the probability of both tossing a head on the coin and drawing a red bead is (1/3) * (7/16) = 7/48.
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