A bag of marbles contains 5 red, 3 blue, 2 yellow, and 4 orange marbles. An event is defined as drawing a marble of colour A out of the bag, replacing it, and then drawing a marble of colour B. The probability of this event is 0.06.Given that probability of drawing a marble of colour A is 0.21, colour B is most likelyared bbluecyellow dorange
Question
A bag of marbles contains 5 red, 3 blue, 2 yellow, and 4 orange marbles. An event is defined as drawing a marble of colour A out of the bag, replacing it, and then drawing a marble of colour B. The probability of this event is 0.06.Given that probability of drawing a marble of colour A is 0.21, colour B is most likelyared bbluecyellow dorange
Solution
To solve this problem, we need to use the formula for the probability of two independent events, which is P(A and B) = P(A) * P(B).
We know that P(A and B) = 0.06 and P(A) = 0.21. We can substitute these values into the formula and solve for P(B):
0.06 = 0.21 * P(B)
To solve for P(B), divide both sides of the equation by 0.21:
P(B) = 0.06 / 0.21 = 0.2857
This means that the probability of drawing a marble of colour B is 0.2857.
Now, we need to determine which colour of marble is most likely to have this probability. The total number of marbles in the bag is 5 (red) + 3 (blue) + 2 (yellow) + 4 (orange) = 14 marbles.
The probability of drawing each colour of marble is:
- Red: 5/14 = 0.3571
- Blue: 3/14 = 0.2143
- Yellow: 2/14 = 0.1429
- Orange: 4/14 = 0.2857
Therefore, the marble of colour B is most likely to be orange.
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