#1 A coin will be tossed 10 times. Find the chance that there will be exactly 2 heads among the first 5 tosses, and exactly 4 heads among the last 5 tosses.
#2 An 11-digit number is randomly chosen by drawing 11 times from a box that has one ticket for each of the numbers 0 to 9 and writing down the numbers on the tickets in the order in which they are drawn. Find the chance that exactly 4 of the digits in the number chosen are five.
Question 1:
The number of heads in the first 5 tosses could be modelled as:
Similarly for last 5 tosses, we have the distribution as:
Also as the first 5 tosses are independent of the last 5 tosses, the required probability here is computed as:
Therefore 0.0488 is the required probability here.
Question 2:
Here as each of the 11 digits is equally likely to be any digit from 0 to 9, therefore for each draw there is a probability of 0.1 to get a digit five. The number of fives in 11 draws could be modelled here as:
Therefore now the required probability is computed here as:
Therefore 0.0158 is the required probability here.
#1 A coin will be tossed 10 times. Find the chance that there will be exactly...
a coin is tossed 12 times then what is the probability at most 4 of the tosses are heads? what is the probability of the heads number more than 4 and less than 7? four balls are drawn at random from a box containing 2 red 2 white and 1 yellow balls what is the probability that the remaining ball is red
a fair coin is tossed three times. A. give the sample space B. find the probability exactly two heads are tossed C. Find the probability all three tosses are heads given that the last toss is heads
3. (3 points) A coin is tossed 10 times. Find the chance of getting 6 heads and 4 tai
1. A fair coin is tossed three times. Let A be the event that there are at least two heads in the three tosses and let B be the event that there are exactly two heads among the three tosses. a. Draw the complete tree diagram for this experiment. [3] b. What are the sample space and probability function for this experiment? [5] c. Compute P(A), P(B), P(A|B), and P(B|A). [7]
1. A fair coin is tossed three times. Let A be the event that there are at least two heads in the three tosses and let B be the event that there are exactly two heads among the three tosses. a. Draw the complete tree diagram for this experiment. [3] b. What are the sample space and probability function for this experiment? [5] c. Compute P(A), P(B), P(A|B), and P(B|A). [7]
A coin is tossed 1,000 times. What is the chance that the number of heads will be between 495 to 505?
7.) Suppose that a fair coin is tossed 10 times and lands on heads exactly 2 times. Assuming that the tosses are independent, show that the conditional probability that the first toss landed on heads is 0.2. 8.) Suppose that X is uniformly distributed on [0,1] and let A be the event that X є 10,05) and let B be the event that X e [0.25,0.5) U[0.75,1.0). Show that A and B are independent.
A fair coin is tossed 10 times. Part A. What is the probability of obtaining exactly 5 heads and 5 tails? Part B. What is the probability of obtaining between 4 and 6 heads, inclusive?
a. Suppose that a fair coin is tossed 15 times. If 10 heads are observed, determine an expression / equation for the probability that 7 heads occurred in the first 9 tosses. b. Now, generalize your result from part a. Now suppose that a fair coin is to be tossed n times. If x heads are observed in the n tosses, derive an expression for the probability that there were y heads observed in the first m tosses. Note the...
A fair coin is tossed 20 times. Let X be the number of heads thrown in the first 10 tosses, and let Y be the number of heads tossed in the last 10 tosses. Find the conditional probability that X = 6, given that X + Y = 10.