The following experiment is used to check a person who claims to have powers of mental telepathy. Six cards are numbered 1 through 6. Seat the person being tested on one side of a screen and a person who will select a card on the other side. The person with the cards shuffles them, selects one at random, and turns it up. The person being tested "receives vibes" and tells which number he thinks is turned up. The card is replaced, and the process is repeated for a total of six times. (Round your answers to four decimal places.) (a) Based on random chance alone, find the probability that the person being tested identifies all six numbers correctly. (b) Based on random chance alone, find the probability that the person being tested identifies all six numbers incorrectly. (c) Based on random chance alone, find the probability that the person being tested identifies at least one of the six numbers correctly. (d) Based on random chance alone, if this sequence is repeated three times and each time the person being tested identifies at least one of the sequence of six numbers correctly, would you say this supports powers of mental telepathy? The probability of identifying at least one correctly at all times is ; therefore, this ---Select--- support the powers of mental telepathy.