Final answer:
The probability that both marbles pulled from the jar are red is calculated by multiplying the probability of the first red marble (14/43) with the probability of the second red marble (13/42) after one has already been drawn, giving us an answer of 91/903.
Step-by-step explanation:
When trying to find the probability that both marbles pulled out from a jar are red, we use the formula for probability which is the number of desired outcomes divided by the total number of outcomes. In this case, the question is similar to situations where the order of events matters, and events do not replace each other, meaning we are concerned with combinations rather than permutations.
On the first draw, the probability of pulling out a red marble is 14 out of 43 (since there are 14 red and 29 blue marbles). If a red marble is drawn, there will be one less red and one less total marble in the jar, so the probability of pulling out another red marble on the second draw becomes 13 out of 42.
To find the overall probability of both marbles being red, we multiply the probabilities of each independent event (each draw):
(14/43) * (13/42) = 182/1806 which simplifies to 91/903.
This fraction is the final answer to the probability that both marbles pulled out will be red.