John has 3 unique coins such that the probability of obtaining a head when the coin is flipped is 110, 210 and 310, respectively. If he flips each of the 3 coins once, the probability that at least 1 heads appears is p. What is the value of 1000p?
496...............:)
Your numbers are nuts, so I assume it should read 0.110, 0.210, 0.310 as the probabilities of Head.
pr(at least once)=1-pr(no heads)
= 1- (.890)(.790)(.690)=.515
1000p=515
Well, if John has 3 unique coins, I hope they don't start arguing about which one is the shiniest or the most valuable. That could get awkward!
Now, let's solve the probability problem here. The probability of obtaining a head when the first coin is flipped is 110, for the second coin is 210, and for the third coin is 310.
To find the probability that at least 1 head appears when flipping all three coins, you can calculate the probability that no heads appear (tails on all three flips) and subtract it from 1.
The probability of no heads appearing when flipping one coin is 1 - 110 = 0.9. Since the coins are unique, the probabilities are independent, so the probability of no heads appearing on all three coins is 0.9 * 0.9 * 0.9 = 0.729.
Therefore, the probability that at least 1 head appears is 1 - 0.729 = 0.271.
Now, to find 1000p, we multiply the probability p by 1000. So, 1000 * 0.271 = 271.
Therefore, the value of 1000p is 271.
To solve this problem, we need to calculate the probability that at least one head appears when flipping each of the three coins.
First, let's calculate the probability of getting tails for each coin. The probability of obtaining a head is given as 110, 210, and 310 for the three coins.
The probability of getting tails for each coin is simply 1 minus the probability of getting heads.
For the first coin:
Probability of tails = 1 - (110/1000) = 1 - 0.11 = 0.89
For the second coin:
Probability of tails = 1 - (210/1000) = 1 - 0.21 = 0.79
For the third coin:
Probability of tails = 1 - (310/1000) = 1 - 0.31 = 0.69
Since getting tails on each coin is independent of each other, we can simply multiply the probabilities of getting tails on each coin to find the probability that all three coins show tails.
Probability of getting tails on all three coins = 0.89 * 0.79 * 0.69 = 0.486229
Now, since we are interested in the probability of at least one head appearing, we can subtract the probability of all three coins showing tails from 1.
Probability of at least one head = 1 - 0.486229 = 0.51377
Finally, to find the value of 1000p, we multiply the probability by 1000.
1000p = 1000 * 0.51377 = 513.77
Therefore, the value of 1000p is 513.77.