Answer: the probability that fewer than 100 in a random sample of 818 men are bald is 0.9830
Step-by-step explanation:
Given that;
p = 10% = 0.1
so let q = 1 - p = 1 - 0.1 = 0.9
n = 818
μ = np = 818 × 0.1 = 81.8
α = √(npq) = √( 818 × 0.1 × 0.9 ) = √73.62 = 8.58
Now to find P( x < 100)
we say;
Z = (X-μ / α) = ((100-81.8) / 8.58) = 18.2 / 8.58 = 2.12
P(x<100) = P(z < 2.12)
from z-score table
P(z < 2.12) = 0.9830
Therefore the probability that fewer than 100 in a random sample of 818 men are bald is 0.9830
So we know that the dice had 6 numbers which is 1 to 6, and we know that the odd number between 1 and 6 is 1,3,5. As a result, the probability of rolling an odd number on a fair die is 3/6 or 1/2, and we already know that probability of flipping a tail on a coin is 1/2, so I just take 1/2 times 1/2 to get 1/4 which is C. Hope it help!
Answer:
8n^8
Step-by-step explanation:
n3*2*n5*4
=8*n8
8n^8
Answer:
(i) A truth table shows how the truth or falsity of a compound statement depends on the truth or falsity of the simple statements from which it's constructed.
Since A ∧ B (the symbol ∧ means A and B) is true only when both A and B are true, its negation A NAND B is true as long as one of A or B is false.
Since A ∨ B (the symbol ∨ means A or B) is true when one of A or B is true, its negation A NOR B is only true when both A and B are false.
Below are the truth tables for NAND and NOR connectives.
(ii) To show that (A NAND B)∨(A NOR B) is equivalent to (A NAND B) we build the truth table.
Since the last column (A NAND B)∨(A NOR B) is equal to (A NAND B) it follows that the statements are equivalent.
(iii) To show that (A NAND B)∧(A NOR B) is equivalent to (A NOR B) we build the truth table.
Since the last column (A NAND B)∧(A NOR B) is equal to (A NOR B) it follows that the statements are equivalent.
Answer:
a) 0.8333
b) 0.75
c) 0.8181 or 0.9090
Step-by-step explanation:
a)
The probability the visitor selects an authentic painting is
10/12 = 0.8333
b)
Since the opinion of the expert does not depend on your choice, the events are <em>independent</em>, so the probability that the expert says is authentic and it really is, is
0.8333*0.9 = 0.75
c)
If the expert decides the painting is a copy and it is not, then there are 11 paintings of which 9 are authentic, so the probability the visitor selects a new original painting is
9/11= 0.8181
If the expert decides the painting is a copy and it is, then there are 11 paintings of which 10 are authentic, so the probability the visitor selects a new original painting is
10/11= 0.9090
