dreamerchaser wrote:
Anyone can help to solve this question in an understandable way
Let me try:
To answer the question we need to find:
Number of occurrences when Paul's result is same as Richard's alone,
or Quinn's alone . "Or" is used because question stem is "What is the probability that Paul's result is
the same as at least one of the other two results?". Had the question been "What is the probability that Paul's result is the same as two other players'?" we needed to calculate different number.
The probability that Event A (Paul's toss is the same as Richard's) or Event B (Paul's toss is the same as Quinn's) occurs is equal to the probability that Event A occurs plus the probability that Event B occurs minus the probability that both Events A and B occur (that is Paul's toss is the same as Q's and R's ).
Lets start
1. When tossed, a coin lands either heads(H) or tails(T), so 2 options exist per a single coin toss.
2. When 3 coins are tossed simultaneously, number of possible
different combinations = 2*2*2 = 2^3= 8. All possible different combinations (letters correspond to Gold, Silver and Bronze coins respectively):
HHH
HHT
HTH
HTT
THH
TTH
TTT
THT
3. We need not to calculate how many combinations Paul will have when he tosses his coins, because for any combination of his coins, number of different combinations for R and Q is always the same and equal to 8.
Therefore,
1.probability that Paul's toss is the same as R's = 1/8
2. probability that Paul's toss is the same as Q's = 1/8
3. probability that Paul's toss is the same as Q's and R's = ? Now to answer this question we need to find how many different combinations R's and Q's could have = 8*8 = 64, therefore, the probability = 1/64
The probability that Event A or Event B occurs is equal to the probability that Event A occurs plus the probability that Event B occurs minus the probability that both Events A and B occur.
=> 1/8+1/8-1/64 = 15/64
Different approach would be to calculate probability of that Paul's toss is not the same as either R's or Quinn =event C and subtract C from 1 to get the answer. (1-eventC), which is shown by
philipssonicare