Therefore, the probability that the second ball is red given that the first We can use the fact that sets of branches must add up to 1 as a way ofĬhecking our answer. s e c o n d b a l l i s r e d fi r s t b a l l i s r e d n u m b e r o f r e d b a l l s a f t e r a r e d b a l l i s s e l e c t e d t o t a l n u m b e r o f b a l l s a f t e r a r e d b a l l i s s e l e c t e dĪs we are told in the problem that the probability of the second ball beingīlue given that the first ball is red is 3 9, then So, the probability that the secondīall will be red is calculated by taking the number of red balls in the bagĪfter a red ball (6) is selected and dividing it by the total number ofīalls after a red ball is selected (9), as follows: Selected first, then there will be 6 red balls in the bag now, but the Selected is red, then we need to use the information that a red ball is firstĪt the start, there are 3 blue balls and 7 red balls. The probability that the second ball selected is red given that the first ball When calculating the probability of the outcome in the second event.Īs we are required to find the value of □, which represents As such, we need to consider what the outcome of the first event is This means that the colour of the second ball is dependent on the colour of theįirst ball. We are told from the question that two balls are selected □ that represents the probability that the second ball Given that the first ball is red, find the value of Further, if we have the probability of □ given thatīranches, then the other branch must be the probability of Pair of branches, then the other branch must be the probability of □ given that □ has occurred as one of the Then the second branch of the pair must be the probability of With the first branch of the pair being the probability of □, As such, if we have two outcomes of an event, ![]() In a treeĭiagram, each set of branches must add up to 1, since the probabilities of all Using these rules of probability, we can apply them to a tree diagram. The complement of event □ is sometimes also written as
0 Comments
Leave a Reply. |